# Machine Learning of Time Series Using Time-delay Embedding and Precision Annealing

arXiv: https://arxiv.org/abs/1902.05062 · HTML: https://mlsanity.com/paper/1902.05062/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Forecasting Using Reservoir Computing: The Role of Generalized Synchronization](https://mlsanity.com/paper/2102.08930/) (2021)
- [What They Saw, Not Just Where They Looked: Semantic Scanpath Similarity via VLMs and NLP metric](https://mlsanity.com/paper/2604.08494/) (2026)

## Abstract (arXiv)

Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. Using the equivalence between statistical data assimilation and supervised machine learning, we revisit this task. The training method for the machine utilizes a precision annealing approach to identifying the global minimum of the action (-log[P]). In this way we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn); tn = t0 + n Delta t and using methods of nonlinear time series analysis show how to produce a DE > 1 dimensional time delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space we explore the use of feed forward multi-layer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs.